Chapter 4, Problem 55R

To determine

To calculate: Power needed to climb.

Answer to Problem 55R

Power need to make the climb is $\underset{\_}{300\text{ W}}$ .

Explanation of Solution

Given:

Weight = $500\text{ N}$

Height = $\text{3 m}$

Time = $\text{5 s}$

Formula used:

Potential energy is given by,

$PE=mgh$

where $m$ is mass, $g$ is acceleration due to gravity and $h$ is height.

Power is given by,

$P=\frac{E}{t}$

where $E$ is energy and $t$ is time.

Calculation:

To calculate power, first calculate energy.

Energy is calculated as:

$\begin{array}{l}PE=mgh\\ =(500\text{ N)(3 m)}\\ \text{ =1500 J}\end{array}$

Power is calculated as:

$\begin{array}{l}P=\frac{E}{t}\\ =\frac{1500\text{ J}}{5\text{ s}}\\ =300\text{ W }\end{array}$

Conclusion:

Power need to make the climb is $\underset{\_}{300\text{ W}}$